1. Field of the Invention
The present invention relates to a stability control system for use in an automatic control system, more particularly to the stability control system using a modern control to ensure a follow-up performance and a stability of the automatic control system.
2. Description of the Related Arts
In general, an automatic control system is provided for operating a controlled system automatically so as to adapt it to a desired state. As for an ordinary system performed in the automatic control system, is employed a PID (Proportional, Integral and Derivative) control system which is included in a so-called classical control system. The PID control system is a control system which is processed on the basis of characteristics in a frequency domain, and can be processed as a physical quantity, so that it has been utilized in various fields for a long time.
In contrast with the classical control system, is getting popular a modern control system which is processed on the basis of characteristics in a time domain, and in accordance with a mathematical principle. The modern control system is a system which is based upon a state-space system, as explained on pages 82-83 of a Japanese publication titled "Syouryoku to Jidouka" (Labor saving and Automation), published in December, 1992 by OHM Sha, for example. In the modern control system, a Hardy space (abbreviated as "H") is proposed, and combined with ".infin." (infinity) representing a norm of distance thereby to provide a "H.infin. control" (H-infinity control). With respect to the norm, it is described that a distance (X.sup.2 +y.sup.2).sup.1/2 on a plane (x, y) is referred to as a second norm, or "2 norm", while .vertline.x.vertline.+.vertline.y.vertline. is referred to as "1 norm". Then, the ".infin." is meant by ".infin. norm", so that it corresponds to MAX (.vertline.x.vertline.,.vertline.y.vertline.), i.e., a lager one out of the absolute value on the x coordinate and the absolute value on the y coordinate is used for the norm. Accordingly, it has been proposed to apply the H.infin. control to a Robust stability control, which is adapted to control a control system in a stable state, even in the case where a state-variation of the system is caused by a disturbance or the like.
As for a combination of the H.infin. control and the PID control, "PID Control Design by Model Matching in Frequency Domain" was proposed in a paper (on pages 201-204) provided for "The 17th Dynamical System Theory Symposium" held in Chiba Prefecture, Japan, during Nov. 30 to Dec. 2, 1994. It is described in the paper that there was a problem when a designed H.infin. controller was installed in an actual apparatus, such that its order came to be higher than the PID controller, or the like. It is further described that in view of a reliability of the controller, maintenance such as re-tuning or the like, and a cost for installation, it would be appropriate to design a controller with a simple operating principle, so that a method for reducing the order of a higher order controller would be important. Accordingly, the paper presents a method for tuning a PID control gain, by specifying a frequency response characteristic of a loop transfer function as a reference model, and matching a loop transfer function of the PID control system with the reference model. With respect to the loop transfer function used for the reference model, the paper describes that it is possible to employ the loop transfer function obtained through the H.infin. control or the like. Thus, the paper proposes the reduction method for the PID controller of the higher order controller. Also, it is described in the paper that it would be possible to designate a frequency band for the matching operation, so that the proposed method would constitute a reduction method for a controller weighted by frequency. In practice, are described a first step to design a stability controller using the H.infin. control or H.sub.2 control and provide the loop transfer function obtained by the controller as the reference model, a second step to hypothesize the structure of the PID controller, and a third step to obtain a gain intersection frequency and a phase intersection frequency of the reference model, and designate a frequency band for matching the loop transfer function of the PID control system (steps 4-9 are omitted, herein). Then, employing an example applied to the controlled system in a vibration system, it is concluded that the PID controller can be designed to keep the performance of the H.infin. controller in part, if the matching frequency band is appropriately set.
As described before, the H.infin. control relates to the least value problem of the infinity norm as defined in the complex function space called Hardy space, and requires complicated computation repeatedly, so that the controller necessarily comes to be of higher order. By simplifying the design algorithm, it has become possible to reduce the order, recently. With respect to the controlled system having a lot of singular points, however, its computing process time would be prolonged, so that its application would be difficult.
According to the method as described in the paper, the reduction could be made, but the method was to limit a frequency band for model matching with a certain H.infin. controller to a range in which there is no unstable factor. Nothing is described in the paper about identification of the system, i.e., a method for obtaining the H.infin. controller itself is not described. Therefore, the control having a range out of that range can not be performed. The greater that range was expanded, the farther the control would remote from that region. In order to improve the Robust stability control, a lead/lag compensator must be used together. Accordingly, the prior method is not necessarily appropriate to the controlled system having a plurality of resonance points and anti-resonance points.
After all, while the H.infin. controller was used in the prior method described in the paper, the controlled system would be limited in view of the limit to the processing time, so that the application of the H.infin. controller would be very limited. If priority is given to shortening the processing time in the prior method, approximate accuracy will be lessened, so that it will not be easy to harmonize them.